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Use of transformed auxiliary variable in estimating the finite population mean. (English) Zbl 0963.62014
Summary: For estimating the finite population mean \(\overline Y\) of the study character \(y\), an estimator using a transformed auxiliary variable has been defined. The bias and mean-squared error (MSE) of the proposed estimator have been obtained. The regions of preference have been obtained under which it is better than the usual unbiased estimator \(\overline y\), the ratio estimator \(\overline y_R=\overline y\overline X/ \overline x\), the B.V.S. Sisodia and V.K. Dwivedi estimator [J. Ind. Soc. Agricult. Stat. 33, 13-18 (1981)], \(\overline y_s=\overline y(\overline X+ C_x)/(\overline x+C_x)\), and the H.P. Singh and M.S. Kakran estimator [submitted to ibid.)], \(\overline y_k=y(\overline X+\beta_2(x))/(\overline x+\beta_2(x))\). An empirical study has been carried out to demonstrate the superiority of the suggested estimator over the others.

62D05 Sampling theory, sample surveys
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